Paper Citation Record · LEDGER

Multiprecision computing for multistage fractional physics-informed neural networks

As of 15 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2505.22377.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.22377 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:17:10.000690Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

21 of 21 outbound references displayed

verified exact0
verified fuzzy8
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ab31a7e9-855a-46cc-88ce-a660ea6de7e2 · outbound

This paper cites Cuomo, V.

Multiprecision computing for multistage fractional physics-informed neural networks Cuomo, V

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:12.848694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 365eeb4a-f51b-4fd0-8ed0-049f65d02437 · outbound

This paper cites Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling.

Multiprecision computing for multistage fractional physics-informed neural networks Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T13:17:08.010206Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea5853a1-f9c1-4af8-995f-e7a4a0a9c6b1 · outbound

This paper cites Stacked networks improve physics-informed training: applications to neural networks and deep operator networks.

Multiprecision computing for multistage fractional physics-informed neural networks Stacked networks improve physics-informed training: applications to neural networks and deep operator networks

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T13:17:08.089650Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c263a844-dc6a-4cb9-b8ab-7bb4aef13b6b · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Multiprecision computing for multistage fractional physics-informed neural networks Adam: A Method for Stochastic Optimization

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T13:17:08.175051Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 575014b0-c9ad-4eb1-9686-ad869d491254 · outbound

This paper cites Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains.

Multiprecision computing for multistage fractional physics-informed neural networks Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T13:17:08.348854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fde3f472-2127-4b5f-9702-56f3cae81da0 · outbound

This paper cites an unresolved cited work.

Multiprecision computing for multistage fractional physics-informed neural networks Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:17:12.691318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 69460fb7-0047-4924-b1ef-a8eb6ea4cbd3 · outbound

This paper cites an unresolved cited work.

Multiprecision computing for multistage fractional physics-informed neural networks Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:17:12.548080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 04582916-bbcb-4da1-be1c-86a8b8c201b0 · outbound

This paper cites Metzler and J.

Multiprecision computing for multistage fractional physics-informed neural networks Metzler and J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:12.390476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f47ca6e4-c32c-4f4f-a336-4f9c0e4aa060 · outbound

This paper cites an unresolved cited work.

Multiprecision computing for multistage fractional physics-informed neural networks Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:17:12.157503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d3df8903-d71b-4fab-a5be-7b6fbb8e0403 · outbound

This paper cites an unresolved cited work.

Multiprecision computing for multistage fractional physics-informed neural networks Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:17:12.022443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6b8dd274-c0a1-4da1-a9d1-704bb21c02c5 · outbound

This paper cites Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.

Multiprecision computing for multistage fractional physics-informed neural networks Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T13:17:08.987858Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 801d2fa8-e382-4b36-a5cb-655a4caed22f · outbound

This paper cites Raissi, P.

Multiprecision computing for multistage fractional physics-informed neural networks Raissi, P

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T13:17:09.106590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdc64237-c37a-4a39-9e69-89be5c0947b9 · outbound

This paper cites an unresolved cited work.

Multiprecision computing for multistage fractional physics-informed neural networks Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:17:11.805991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 86acc44d-d9ae-4e84-baae-f476fd6afd18 · outbound

This paper cites Stynes, E.

Multiprecision computing for multistage fractional physics-informed neural networks Stynes, E

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:11.608899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 50ec41a2-415c-48b5-beac-8813186a55a3 · outbound

This paper cites Tancik, P.

Multiprecision computing for multistage fractional physics-informed neural networks Tancik, P

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:11.423627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a06a2ed2-ef9c-49a7-ae19-f98232f59f82 · outbound

This paper cites From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning.

Multiprecision computing for multistage fractional physics-informed neural networks From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T13:17:09.550257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57c2a76a-4969-4d94-860e-b4691696b5b1 · outbound

This paper cites W ang, Y.

Multiprecision computing for multistage fractional physics-informed neural networks W ang, Y

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:11.188774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a65d5062-11a2-4458-a5df-a07b31b50d0f · outbound

This paper cites W ang, H.

Multiprecision computing for multistage fractional physics-informed neural networks W ang, H

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:10.962049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8235f8d1-3094-4e73-980d-81b4c5f8e863 · outbound

This paper cites W ang and C.-Y.

Multiprecision computing for multistage fractional physics-informed neural networks W ang and C.-Y

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:10.740871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c6c5bf1b-a939-4c12-9614-60f1eb7f4807 · outbound

This paper cites Xu and M.

Multiprecision computing for multistage fractional physics-informed neural networks Xu and M

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:17:10.579164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 38d9966d-f8bd-4b34-84bf-a33f9cb7a523 · outbound

This paper cites an unresolved cited work.

Multiprecision computing for multistage fractional physics-informed neural networks Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:17:10.331340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

No inbound Pith citation observations are available.